docs: def contraction_beveled(Di1, Di2, l=None, angle=None):
      r'''Returns loss coefficient for any sharp beveled pipe contraction
      as shown in [1]_.
  
      .. math::
          K = 0.0696[1+C_B(\sin(\alpha/2)-1)](1-\beta^5)\lambda^2 + (\lambda-1)^2
  
      .. math::
          \lambda = 1 + 0.622\left[1+C_B\left(\left(\frac{\alpha}{180}
          \right)^{0.8}-1\right)\right](1-0.215\beta^2-0.785\beta^5)
  
      .. math::
          C_B = \frac{l}{d_2}\frac{2\beta\tan(\alpha/2)}{1-\beta}
  
      .. math::
          \beta = d_2/d_1
  
      .. figure:: fittings/contraction_beveled.png
         :scale: 30 %
         :alt: contraction beveled; after [1]_
  
      Parameters
      ----------
      Di1 : float
          Inside diameter of original pipe, [m]
      Di2 : float
          Inside diameter of following pipe, [m]
      l : float
          Length of the bevel along the pipe axis ,[m]
      angle : float
          Angle of bevel, [degrees]
  
      Returns
      -------
      K : float
          Loss coefficient in terms of the following pipe [-]
  
      Notes
      -----
  
      Examples
      --------
      >>> contraction_beveled(Di1=0.5, Di2=0.1, l=.7*.1, angle=120)
      0.40946469413070485
  
      References
      ----------
      .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical
         and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.
      '''
      angle = radians(angle)
      beta = Di2/Di1
      CB = l/Di2*2.0*beta*tan(0.5*angle)/(1.0 - beta)
      beta2 = beta*beta
      beta5 = beta2*beta2*beta
      lbd = 1.0 + 0.622*(1.0 + CB*((angle/pi)**0.8 - 1.0))*(1.0 - 0.215*beta2 - 0.785*beta5)
      return 0.0696*(1.0 + CB*(sin(0.5*angle) - 1.0))*(1.0 - beta5)*lbd*lbd + (lbd-1.0)**2